Question

$0.\overline{5} + 0.19\overline{4}$.

Answer 1

0.75

Explanation:

Answer 2

`0.\overline{5} + 0.19\overline{4}=0.75`

Explanation:

Given expression:

`0.\overline{5} + 0.19\overline{4}`

To evaluate the expression.

Solution.

The values are

`0.\overline{5}=0.555555......`

Let
`X=0.555555.....` -----------1

Multiplying 10 both sides.

`10X=5.555555....`----------2

Subtracting 1 from 2.

`10X=5.555555....`

-
`X=0.555555.....`

-------------------------------------------

`9X=5.0`

Dividing both sides by 9.

`(9X)/(9)=(5)/(9)`

`X=(5)/(9)`

`0.19\overline{4}=0.194444....`

Let
`Y=0.1944444..`

Multiplying both sides by 100

`100Y=19.44444..`------------3

Multiplying 1000 both sides.

`1000Y=194.4444....`----------4

Subtracting 3 from 4.

`1000Y=194.4444....`

-
`100Y=19.44444.....`

-------------------------------------------

`900Y=175.0`

Dividing both sides by 900.

`(900Y)/(900)=(175)/(900)`

`Y=(175)/(900)`

So, we can evaluate the given expression as:

⇒
`0.\overline{5} + 0.19\overline{4}`

⇒
`X+Y`

⇒
`(5)/(9)+(175)/(900)`

Taking LCD = 900

⇒
`(5* 100)/(9* 100)+(175)/(900)`

⇒
`(500)/(900)+(175)/(900)`

Adding numerators.

⇒
`(500+175)/(900)`

⇒
`(675)/(900)`

⇒
`0.75` (Answer)